Is it permissible for a woman to use a contraceptive without telling her husband although he wants to have as many children as possible and she can`t care for them?
All perfect praise be to Allah, the Lord of the Worlds; may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
If the pregnancy is harmful to the woman, it is permissible for her to use a contraceptive; however, this has to be backed by a medical report from a God-fearing doctor. In addition, you had better inform your of what you are doing to avoid dispute. And Allah The Almighty Knows Best.
Is it permissible for one to give the Zakah(obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his indebted , or poor brother.
Is it permissible for the doctor to uncover the hair of a female patient out of necessity?
It is only permissible for him to do so when there is no female doctor, and he should examine the patient in the presence of one of her Mahrams(unmarriageable kin).
Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.